Numerical simulation of flow modeling in ducted axial fan using simpson’s 13rd rule

International Journal of Advanced Research in Engineering and Technology RESEARCH IN–
INTERNATIONAL JOURNAL OF ADVANCED (IJARET), ISSN 0976
6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME
ENGINEERING AND TECHNOLOGY (IJARET)

ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online) IJARET
Volume 3, Issue 1, January- June (2012), pp. 107-117
© IAEME: www.iaeme.com/ijaret.html ©IAEME
Journal Impact Factor (2011): 0.7315 (Calculated by GISI)
www.jifactor.com

NUMERICAL SIMULATION OF FLOW MODELING IN DUCTED
AXIAL FAN USING SIMPSON’S 1/3rd RULE

Manikandapirapu P.K.1 Srinivasa G.R.2 Sudhakar K.G.3 Madhu D. 4
1
Ph.D Candidate, Mechanical Department, Dayananda Sagar College of Engineering, Bangalore.
2
Professor and Principal Investigator, Dayananda Sagar College of Engineering, Bangalore.
3
Dean (Research and Development), CDGI, Indore, Madhya Pradesh .
4
Professor and Head, Mechanical Department, Government Engg. College, KRPET-571426.

ABSTRACT
The paper presents to develop the numerical simulation of flow model for
three dimensional flow and one dimensional flow in Ducted Axial Fan by using the
numerical integral procedure of Simpson’s 1/3rd rule. Main objective of this paper is to
develop the numerical flow model and measure the pressure rise for varying the
functional parameters of inlet velocity, whirl velocity, rotor speed and diameter of blade
from hub to tip in ducted axial fan by using the code of MATLAB for Simpson’s 1/3rd
rule. In this main phase of paper, the analogy of three dimensional flow and one
dimensional flow of numerical flow modeling have been investigated to optimize the
parameter of pressure rise in ducted axial flow fan by using the integration procedure of
Simpson’s 1/3rd rule.
Keywords: Numerical Integration, Simpson’s 1/3rd rule, Pressure rise, Whirl velocity,
Pressure Ratio, Flow ratio, Rotor speed, Axial Fan.

1.0 INTRODUCTION

Mining fans and cooling tower fans normally employ axial blades and or required to
work under adverse environmental conditions. They have to operate in a narrow band of
speed and throttle positions in order to give best performance in terms of pressure rise,
high efficiency and also stable condition. Since the range in which the fan has to operate
under stable condition is very narrow, clear knowledge has to be obtained about the
whole range of operating conditions if the fan has to be operated using active adaptive

107

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –

control devices. The performance of axial fan can be graphically represented as shown in
figure 1.

Fig: 1 Graphical representation of Axial Fan performance curve

2. TEST FACILITY AND INSTRUMENTATION

Experimental setup, fabricated to create stall conditions and to introduce unstall
conditions in an industrial ducted axial fan is shown in figure 2.
ndustrial

Fig: 2 Ducted Axial Fan Rig
A 2 HP Variable frequency 3 3-phase induction electrical drive is coupled to
ical
the electrical motor to derive variable speed ranges. Schematic representation of
ducted fan setup is shown in figure 3.

108


Fig: 3 Ducted Axial Fan - Schematic

The flow enters the test duct through a bell mouth entry of cubic profile. The bell
mouth performs two functions: it provides a smooth undisturbed flow into the duct and
also serves the purpose of metering the flow rate. The bell mouth is made of fiber
reinforced polyester with a smooth internal finish. The motor is positioned inside a 381
mm diameter x 457 mm length of fan casing. The aspect (L/D) ratio of the casing is 1.2.
The hub with blades, set at the required angle is mounted on the extended shaft of the
electric motor. The fan hub is made of two identical halves. The surface of the hub is
made spherical so that the blade root portion with the same contour could be seated
perfectly on this, thus avoiding any gap between these two mating parts. An outlet duct
identical in every way with that at inlet is used at the downstream of the fan. A flow
throttle is placed at the exit, having sufficient movement to present an exit area greater
than that of the duct.
3.0 NUMERICAL ANALYSIS
Numerical analysis is the study of algorithms that use numerical approximation for
the problems of mathematical analysis. In Numerical algorithm is a step-by-step
procedure for calculations. Algorithms are used for calculation, data processing, and
reasoning. More precisely, an algorithm is an effective method expressed as a finite list of
well-defined instructions for calculating a function. Starting from an initial state and
initial input for the instructions describe a computation that, when executed, will proceed
through a finite number of well-defined successive states, eventually producing output
and terminating at a final ending state. Mathematical analysis, which mathematicians
refer to simply as analysis, is a branch of pure mathematics that includes the theories of
differentiation, integration and measure, limits, infinite series, and analytic functions.

109


3.1 MATLAB
MATLAB is a programming environment for algorithm development, data
analysis, visualization, and numerical computation. MATLAB is a wide range of
applications, including signal and image processing, communications, control design, test
and measurement, financial modeling and analysis, and computational biology.
MATLAB contains mathematical, statistical, and engineering functions to support all
common engineering and science operations. These functions, developed by experts in
mathematics, are the foundation of the MATLAB language. The core math functions use
the LAPACK and BLAS linear algebra subroutine libraries and the FFT Discrete Fourier
Transform library. Because these processor-dependent libraries are optimized to the
different platforms that MATLAB supports, they execute faster than the equivalent C or
C++ code.

4.0 FLOW MODELING

The aim of the flow modeling is to measure the pressure rise as a function of
whirl velocity and rotor speed for different diameter of blade from hub to tip in ducted
axial flow fan. In this flow modeling equation helps to optimize the parameter of pressure
rise for different whirl velocity in a ducted axial fan.

4.1 Three Dimensional Flow Equation
ଵ ஼ഇ మ
ሺ‫݌݀ + ݌‬ሻሺ‫ݎ݀ + ݎ‬ሻ݀ߠ − ‫ − ߠ݀ ݎ ݌‬ሺ‫݌݀ + ݌‬ሻ ݀‫= ߠ݀ ݎ‬dm (4.1)
ଶ ௥
ଵ ௗ௣೚ ௗ௖ೣ ௖௾ ௗ
= ܿ௫ + ( ‫ܿ ݎ‬௾ ) (4.2)
ఘ ௗ௥ ௗ௥ ௥ ௗ௥
ଵ ௗ௣ ௗ௩ೌ ௗ௩ೢ
Stagnation pressure rise = + ‫ݒ‬௔ + ‫ݒ‬௪ (4.3)
ఘ ௗ௥ ௗ௥ ௗ௥

‫( ݌‬Vw.U).dr – Va . dVa – Vw. dVw = dp (4.4)

Stagnation Pressure rise = Total Input Power = 500 Watts as an assumption for
this Analytic and simulation studies of ducted Axial Fan. If integrate that equation
4.4, obtain that final form of equation.
మ
௩ೌ మ
௩ೌ
500 ( ‫ݎ‬ଶ – ‫ݎ‬ଵ ) – ቈቀ ଶ ቁ ௥మ – ቀ ଶ ቁ ௥భ ቉ − ቂ ቀ ೢቁ ௥మ − ቀ ೢቁ ௥భ ቃ = ሾ݀‫݌‬ሿ
௩మ ௩మ ଵ
(4.5)

ଶ ଶ ఘ

110


4.2 One Dimensional Flow Equation
మ
௩ೢ
Pressure rise dp = ࣋ ݀‫ݎ‬
௥
࣒ ×૜.૚૝ ×ࡺ
Pressure Rise = dp =࣋ ቀ ቁ ଶ × ‫ݎ݀ ݎ ׬‬ (4.6)
૟૙

5.0 NUMERICAL MODELING
From this flow modeling equation, adopt and continue the procedure of
numerical integration scheme. In this numerical integration procedure, MATLAB
code has computed for developing the pressure rise in ducted axial fan using
Simpson’s 1/3 rule.
Simpson’s 1/3 Rule
௕ ௛
‫׬‬௔ ‫= ݔ݀ݕ‬ ଷ
[y0 + 4(y1 + y3 + y5 + …….. +yn-1) + 2(y2 + y4 + y6 +……. + yn-2) + yn] (5.1)

5.1 MATLAB CODE FOR THREE DIMENSIONAL FLOWS USING
૚
SIMPSON’S RULE
૜
Objective
ଵ
To compute the pressure rise in three dimensional flow equations by using Simpson’s ଷ

rule.
%Three Dimensional Flow equation using simpson’s 1/3rd rule
i=0;
for n=0:1:8;
i=i+1;
r=[0.08255:0.013:0.199];
f=208.62*r;
disp(f);
end
n =input('enter the intervals');
h =(0.199-0.08255)/n;
Vwdw = [17.2216:2.710:38.9181];
s=17.2216;
z=38.9181;
sum=0;
for j=(1:1:n/2);
x=(0.08255-h)+(2*h*j);
sum=sum+(4*Vwdw(j));
if j~=n/2
end
end

111


sum=(sum+s+z);
ans =(sum*h)/3;
disp (ans);
r2=input('enter the final radius');
r1=input(' enter the initial radius');
res= 500*(r2-r1);
disp(res);
answer=res-ans;
disp (answer);
PR= 1.048*(answer);
fprintf(',Pressure Rise in N/m2=%g',PR)

MATLAB OUTPUT FOR SIMPSONS 1/3RD RULE

17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181

17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181

17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181

17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181

17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181

17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181

17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181

17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181

17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181

Enter the intervals 9
2.4455

Enter the final radius 0.186
Enter the initial radius 0.08255
51.7250

49.2795

Pressure Rise in N/m2 = 51.6449

112


5.2 MATLAB CODE FOR ONE DIMENSIONAL FLOW EQUATION
૚
USING SIMPSON’S RULE
૜
Objective
ଵ
To compute the pressure rise in one dimensional flow equation by using Simpson’s ଷ

rule.
%('Simpson 1/3rd rule for one dimensional flow equation ');
i=0;
for n=0:1:8;
i=i+1;
r=[0.08255:0.013:0.199];
f=325.89*r;
disp(f);
end
n =input('enter the intervals');
h =(0.199-0.08255)/n;
Vwdw = [26.9022:4.2366:60.7948];
s=26.9022;
z=60.7948;
sum=0;
for j=(1:1:n/2);
x=(0.08255-h)+(2*h*j);
if j~=n/2
end
end
sum=(sum+s+z);
ans =(sum*h)/3;
disp (ans);
PR= 1.048*(ans);
fprintf(',Pressure Rise in N/m2=%g',PR)

MATLAB RESULTS FOR SIMPSONS 1/3RD RULE

26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948

26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948

26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948

26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948

26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948

113


26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948

26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948

26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948

26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948

Enter the intervals 9
3.8207

Pressure Rise in N/m2=4.00411

5.3 CALCULATION OF ERROR PERCENTAGE

Case 1: Three Dimensional Flows

Theoretical value of pressure rise for three dimensional flow of ducted
Axial fan = 51.5308 N/m2
Numerical Modeling of pressure rise for three dimensional flow
of ducted axial fan using Simpson’s 1/3rd Rule = 51.198 N/m2
்௛௘௢௥௜௧௜௖௔௟ ௏௔௟௨௘ –ே௨௠௘௥௜௖௔௟ ௠௢ௗ௘௟௜௡௚ ௏௔௟௨௘
Error Percentage = (5.2)
்௛௘௢௥௜௧௜௖௔௟ ௏௔௟௨௘

ହଵ.ହଷ଴଼ –ହଵ.ଵଽ଼
Error Percentage = ∗ 100
ହଵ.ହଷ଴଼

Error Percentage (%) = 0.646
Case 2: One Dimensional Flow
Theoretical value of pressure rise for one dimensional flow of ducted
Axial fan = 5.034 N/m2
Numerical Modeling of pressure rise for one dimensional flow
of ducted axial fan using Simpson’s 1/3rd Rule = 4.00411 N/m2
்௛௘௢௥௜௧௜௖௔௟ ௏௔௟௨௘ –ே௨௠௘௥௜௖௔௟ ௠௢ௗ௘௟௜௡௚ ௏௔௟௨௘
Error Percentage = (5.3)
்௛௘௢௥௜௧௜௖௔௟ ௏௔௟௨௘
ହ.଴ଷସ – ସ.଴଴ସଵଵ
Error Percentage = ∗ 100
ହ.଴ଷସ

Error Percentage (%) = 20.45

114


6.0 CONCLUSION
In this paper, an attempt has been made to develop the numerical
simulation of three dimensional flows and one dimensional flow code using
MATLAB in Simpson’s 1/3rd rule for ducted axial fan . It is useful to design the
operating condition of axial fan to measure the parameters of pressure rise as a
function of pressure ratio, rotor speed, and diameter of blade from hub to tip in
ducted axial fan. Further, this work can be extended by working on the flow
simulation characteristic study in control system algorithm. The results so far
discussed, indicate that numerical simulation of flow modeling using Simpson’s
1/3rd rule for ducted axial fan is very promising.

ACKNOWLEDGEMENT
The authors gratefully thank AICTE (rps) Grant. for the financial support of
present work.
NOMENCLATURE
cx = Axial velocity in m/s
ܿఏ = Whirl velocity in m/s
r2 = Radius of blade tip in m
r1 = Radius of blade hub in m
N = Tip speed of the blades in rpm
va = Axial velocity in m/s
dp= P2 - P1 = Pressure rise in N/m2
d = Diameter of the blade in m
ρair = Density of air in kg/m3
vw = Whirl velocity in m/s
η = Efficiency of fan

REFERENCES
[1] Day I J,”Active Suppression of Rotating Stall and Surge in Axial
Compressors”, ASME Journal of Turbo machinery, vol 115, P 40-47, 1993
[2] Patrick B Lawlees,”Active Control of Rotating Stall in a Low Speed
Centrifugal Compressors”, Journal of Propulsion and Power, vol 15, No 1, P 38-
44, 1999

115


[3]C A Poensgen ,”Rotating Stall in a Single-Stage Axial Compressor”, Journal of
Turbo machinery, vol.118, P 189-196, 1996
[4] J D Paduano,” Modeling for Control of Rotating stall in High Speed Multistage
Axial Compressor” ASME Journal of Turbo machinery, vol 118, P 1-10, 1996
[5] Chang Sik Kang,”Unsteady Pressure Measurements around Rotor of an Axial
Flow Fan Under Stable and Unstable Operating Conditions”, JSME International
Journal, Series B, vol 48, No 1, P 56-64, 2005.
[6] A H Epstein,”Active Suppression of Aerodynamic instabilities in turbo
machines”, Journal of Propulsion, vol 5, No 2, P 204-211, 1989
[7] Bram de Jager,”Rotating stall and surge control: A survey”, IEEE Proceedings
of 34th Conference on Decision and control, 1993
[8] S Ramamurthy,”Design, Testing and Analysis of Axial Flow Fan,” M E
Thesis, Mechanical Engineering Dept, Indian Institute of Science, 1975
[9] S L Dixon, Fluid Mechanics and Thermodynamics of Turbo machinery, 5th
ed., Pergamon, Oxford, 1998
[10] William W Peng, Fundamentals of Turbo machinery, John Wiley & sons.Inc,
2008
[11] Curtis F Gerald, Applied Numerical Analysis, 5th Edition, Addison-Wesley
Publishing Company. Inc.1998
[12] Rao V Dukkipati, MATLAB for Mechanical Engineers, First Edition, New
Age International Publishers, 2008

116


AUTHORS

Manikandapirapu P.K. received his B.E degree from Mepco Schlenk
Engineering college, M.Tech from P.S.G College of Technology,Anna
University,and now is pursuing Ph.D degree in Dayananda Sagar College
of Engineering, Bangalore under VTU University. His Research interest
include: Turbomachinery, fluid mechanics, Heat transfer and CFD.

Srinivasa G.R. received his Ph.D degree from Indian Institute of Science,
Bangalore. He is currently working as a professor in mechanical
engineering department, Dayananda Sagar College of Engineering,
Bangalore. His Research interest include: Turbomachinery,
Aerodynamics, Fluid Mechanics, Gas turbines and Heat transfer.

Sudhakar K.G received his Ph.D degree from Indian Institute of Science,
Bangalore. He is currently working as a Dean (Research and
Development) in CDGI, Indore, Madhyapradesh. His Research interest
include: Surface Engineering, Metallurgy, Composite Materials, MEMS
and Foundry Technology.

Madhu D received his Ph.D degree from Indian Institute of Technology
(New Delhi). He is currently working as a Professor and Head in
Government Engineering college, KRPET-571426, Karnataka. His
Research interest include: Refrigeration and Air Conditioning, Advanced
Heat Transfer Studies, Multi phase flow and IC Engines.

117

Numerical simulation of flow modeling in ducted axial fan using simpson’s 13rd rule

Recomendados

Recomendados

Mais conteúdo relacionado

Mais procurados

Mais procurados (14)

Destaque

Destaque (20)

Semelhante a Numerical simulation of flow modeling in ducted axial fan using simpson’s 13rd rule

Semelhante a Numerical simulation of flow modeling in ducted axial fan using simpson’s 13rd rule (20)

Mais de iaemedu

Mais de iaemedu (20)

Numerical simulation of flow modeling in ducted axial fan using simpson’s 13rd rule